The brass is hitting the chamber from a short distance away from the case head all the way up to the shoulder. It is visibly larger in diameter along the entire body length, as compared to Starline brass. If I were to push it any further into the die, I would succeed only in pushing the miniscule shoulder back a bit further, and increasing the neck length. It's not a matter of a few thousandths over correct diameter, it's two hundredths. Starline chambers just fine, and I'm currently using that. If it were to expand much in body diameter, the Lee die wouldn't help at all. It simply doesn't taper enough, not until you get right up to the neck of the case.
The area of the brass that rubs the chamber was confirmed by inking the brass and pushing it as far into the chamber as it could go.
I might try Redding, rcbs, or Lyman for a resizing die next, rather than grinding down what I've got, or ordering anything exotic.
Arnie, your grinding suggestion is what worked for me with a minimum chambered Remington that I own, but I don't think it'll help here. The Lee die is the problem, not the chamber.
P.S.
I just got off the phone with Dave at Lee. He stated simply that the Lee dies aren't made for reforming brass, although other brands of resizing dies may work for reforming. He said that the Lee makes dies to resize after firing factory brass, and the amount of "springback" in the brass was making the cases too large to chamber. In other words, go buy something different if you don't like what we sold you. I still believe that 40-65 dies should be capable of reforming 45-70 brass, since that's what most folks will want to be able to do with them, but that's just me.
Dave's explanation about brass spring back rang a little hollow for me, since the Lee dies are .02" too large, not just .002". These dies may not work for any case that needs more than just neck sizing.